Recovering convex boundaries from blurred and noisy observations

• 成果类型: Article
• 署名作者: Goldenshluger, Alexander; Zeevi, Assaf
• 署名单位: University of Haifa; Columbia University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000326
• 发表日期: 2006
• 页码: 1375-1394
• 关键词: change-point estimation; fourier-transforms; Inverse problems; edges; sets; CONVERGENCE; rates

摘要

We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function f is observed with additive Gaussian white noise. The function f is assumed to have convex support G whose boundary is to be recovered. Rather than directly estimating the intensity function, we develop a procedure which is based on estimating the support function of the set G. This approach is closely related to the method of geometric hyperplane probing, a well-known technique in computer vision applications. We establish bounds that reveal how the estimation accuracy depends on the ill-posedness of the convolution operator and the behavior of the intensity function near the boundary.